Notes on Geometric Morita equivalence of twisted Poisson manifolds

TL;DR

This paper explores Morita equivalence in twisted Poisson manifolds, establishing invariants, gauge equivalence implications, and introducing weak Morita equivalence with leaf correspondence.

Contribution

It introduces the concept of weak Morita equivalence and proves gauge equivalent integrable twisted Poisson manifolds are Morita equivalent.

Findings

Gauge equivalent integrable twisted Poisson manifolds are Morita equivalent

Weak Morita equivalence induces a correspondence between twisted symplectic leaves

Morita invariants are reviewed and analyzed

Abstract

This paper is devoted to the study of Morita equivalence for twisted Poisson manifolds. We review some Morita invariants and prove that integrable twisted Poisson manifolds which are gauge equivalent are Morita equivalent. Moreover, we introduce the notion of weak Morita equivalence and show that if two twisted Poisson manifolds are weak Morita equivalent, there exists a one-to-one correspondence between their twisted symplectic leaves.